Sorry for the naivety of the question, my field is not mathematics. I am writing a script to calculate the derivative of a curve given by a set of
(x,y) points as
(x,y) 1,3 2,2 3,7 4,7 5,8 6,12
I calculate the
dy/dx for each point from the slope over a unit of
y(n+1)-y(n) to produce
(x,dy/dx) 2,-1 3,5 4,0 5,1 6,4
Is it mathematically correct? Do I calculate
The given curve is not a mathematical function but an empirical set of data (say x=time, y=temperature). Is it the correct way to calculate the
dy/dx for the available set of data?
EDIT: Probably, it is meaningless to calculate the slope between two given points. Instead, it is better to draw a curve based on the best fit. Then, we will have a better approximation of the data points where the slope at each point is meaningful.
Am I right? Should I recalculate the
y values based on a best-fit approximation before trying to calculate the slope?